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lesya692 [45]
3 years ago
7

ABCD is a quadrilateral with AB equal and parallel to DC. prove that AD is equal and parallel to BC​

Mathematics
1 answer:
rewona [7]3 years ago
6 0

Answer: see below proof

Step-by-step explanation:

Imagine a diagonal line AC

If AB = DC and AB // DC then angle BAC =

Angle ACD Alternate Interior angles theorem.

Then if AB = AD and angle BAC = angle ACD and AC = AC then triangle ABC is congruent to triangle CDA.

If triangle ABC is congruent to triangle CDA then AD = BC because congruent parts of congruent triangles are congruent.

If triangle ABC is congruent to triangle CDA then angle ACB = angle CAD because congruent parts of congruent triangles are congruent.

If angle ACB = angle CAD then AD // BC because of the alternate interior angles theorem.

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Angle of a triangle measures 115° the other two angles are in the ratio of 4:9 what are the measures of those two angles
nasty-shy [4]

Answer:

20, 45

Step-by-step explanation:

A triangle has 180 degrees interior angle measure. One angle measure 115 so that means the other two angles  must add up to 65.

The remaning angles form a ratio of 4:9. This means we must split 65 into a ratio of. 4:9

A ratio partition parts of something. We can add the ratio intergers to find it full length.

4+9=13.

Divide 65/13=5.

Multiply 5x4 and 5x9 serpately.

We get 20 and 45

6 0
3 years ago
What is the equation of the graph shown?​
OlgaM077 [116]

<em>Greetings from Brasil...</em>

As we have a line, the function will be given by the expression:

F(X) = AX + B

where

<em>A = ΔY/ΔX</em>

<em>B = where the line intersects the Y axis</em>

Looking at the graph we have already concluded that

B = - 3

A = ΔY/ΔX

A = (5 - 3)/(4 - 3)     see attached picture

A = 2

So,

F(X) = AX + B

<h2>F(X) = 2X - 3</h2>

5 0
3 years ago
The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.2 grams with a standard deviat
Sophie [7]

Answer:

12.1%

Step-by-step explanation:

Given that:

Mean (μ) = 20.2 grams and standard deviation (σ) = 0.18 grams.

The z score is a score used to determine the number of standard deviations by which the raw score is above or below the mean. A positive z score means  that the raw score is above the mean and a negative z score means that the raw score is below the mean. It is given by:

z=\frac{x-\mu}{\sigma}

a) For x < 19.99 g:

z=\frac{x-\mu}{\sigma}\\\\z=\frac{19.99-20.2}{0.18} \\\\z=-1.17

From the normal distribution table, P(x < 19.99) = P(z < -1.17) = 0.1210 = 12.1%

The probability that a randomly chosen mouse has a mass of less than 19.99 grams is 12.1%

6 0
3 years ago
Lauren took 12 hours to read a 360 page book. At this rate, how long will it take her to read a 1200 page book?
Sliva [168]

Answer:

About 48 hours or 2 days.

Step-by-step explanation:

360 + 360 = 720 + 360 = 1080 + 360 = 1440

12x4=48

4 0
3 years ago
I will give brainliest to whoever helps me with this question. Also, if you could please explain to me how you solved it I would
Helen [10]

Answer:

i say in blank one its 24cm

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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